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______________ Decimal Numbers 1000 100 ones Thousands Hundreds Units Whole number side on the left 1 1 1 1 = 01 . = .01 = .001 = .0001 10 100 1000 10000 . Tenth Hundredth Thousandth Ten Thousandth Fraction side on right of decimal point The fraction side becomes smaller when move further to the right Decimal Numbers consist of a whole part, decimal point and fraction part For example 0.23, 12.345, and 0.675 are examples of decimal numbers Decimal numbers increase on left side and decrease on the right side of the decimal point Reading and Writing Decimal Numbers • The number of digits after the decimal point will determine the number of decimal places in the number. • The last digit in the number will determine the label used to write decimal numbers in words To write decimal number in words, write the number in words like regular whole numbers then attach the label. EXAMPLE#1 Write 0.4 in words SOLUTION: 0.4 has one digit to the left of the decimal point. Therefore the label is tenth 0.4 read as four tenth EXAMPLE#2 Write 0.35 in words SOLUTION: 0.35 has two digits after the decimal point so the label is hundredth. 0.35 is read as thirty five hundredth EXAMPLE#3 Write the number 0.247 in words SOLUTION: 0.247 has three decimal places, therefore the label is thousandth 0.247 read as two hundred forty seven thousandth EXAMPLE#4 Write 0.0027 in words SOLUTION: 0.0027 has four decimal places after the decimal point: therefore the label is ten thousandth 0.0027 is twenty seven ten- thousandth EXAMPLE#5 Write 123.36 in words SOLUTION: 123.36 have two decimal places. The word ‘and’ is used to represent the decimal point. 123.36 read as one hundred twenty three and thirty six hundredth. Page#2 Practice Exercises#1 Write the following in words (1) 0.7 (2) 0.67 (3) 0.569 (4) 0.0006 (5) 567.69 Write Decimals Numbers as Fractions (1) Decimal numbers less than 1 • • • Decimal numbers less than1 has zero on the whole number side Decimal number less than 1 is a proper fraction( denominator larger than the numerator) The number of decimal places will determine the number of zeros in the denominator EXAMPLE#6 Express 0.7 as a fraction SOLUTION: 0.7 has one decimal place so this means tenth or one zero in the denominator 7 0.7 = is a proper fraction 10 EXAMPLE#7 Express 0.35 SOLUTION: 0.35 is two decimal places which means hundredth two zeros 35 7 0.35 = is reduced as proper fraction 100 20 EXAMPLE#8 Express 0.237 as a fraction SOLUTION: 0.237 is a three decimal place number this means thousandth. Three zeros in the denominator. 237 0.237 = 1000 EXAMPLE#9 Express 0.000024 as a fraction SOLUTION: 0.000024 has six decimal places therefore six zeros at the bottom of the fraction 24 3 reduced as 0.000024 = 1000000 125000 Practice Exercises#2 Express the following as a fraction (a) 0.06 (b) 0.25 (c) 0.234 (d) 0.00245 Page#3 Note: Decimal numbers ending with zero. If zero is the last digit in the number, the zero can be dropped Example 0.230 is the same as 0.23. When the zeros are in front of or between nonzero digits, it cannot be dropped from the number. Example 0.02 the 0 is in the tenth place and cannot be dropped. This number has two decimal places. Example 12.304 the 0 is in second place and it cannot be dropped (2) Decimals Greater Than One • • Decimal numbers greater than 1 are mixed fractions which can be express as a improper fractions Convert the decimal part to a fraction using the number of decimal places to determine the number of zeros EXAMPLE#10 Express 2.3 as a fraction SOLUTION: 2.3 one decimal place on the right of the decimal point. 3 2.3 = 2 which is a mixed fraction 10 EXAMPLE#11 Express 1.04 as a fraction SOLUTION: 1.04 is two decimal places = 1 4 1 this reduced as 1 100 25 EXAMPLE#12 Express 26.0271 SOLUTION: In the number 26.0271, 1 is in the ten thousandth place and 26.0271 is a four decimal place number which means four zeros in the denominator 271 26.0271 = 26 10000 Practice Exercises#3 Change the following decimals to a fraction If possible, reduce the fraction (a) 5.24 (b) 4.08 (c) 2.1875 (d) 3.7 (e) 5.0003 (f) 135.124 Page#4 Exercises 1. In the number 0.23457 a. How many decimal places in the number b. What digit is in the tenth place c. What digit is in the thousandth place d. What digit is in the ten-thousandth place 2. Write the decimal numbers in words a. 0.34 b. 0.045 c. 7.08 d. 567.56 e. 68.0567 f. 0.000275 g. 2.5 h. 19.34 3. (a) (b) (c) (d) Write the decimal numbers Nine hundredth Two and three thousandth Seven hundred twenty thousandth Two hundred thirteen and twenty five ten-thousandth 4. (a) (b) (c) (d) (e) (f) Change the decimal numbers to a fraction reduce the fraction to the lowest term 0.66 0.08 7.003 34.75 0.302 13.00025 Answers Page#5 Changing Fractions to Decimals a The fraction can be express as terminating or a non-terminating decimal number. b In order to change fractions to a decimal divide the numerator by the denominator. a =b a b 4 to a decimal number 5 0.8 4 = 0.8 terminating decimal SOLUTION: 4 divided by 5 = 5 4.0 , therefore 5 7 EXAMPLE#14 Change to a decimal 8 0.875 7 SOLUTION: 8 7.000 therefore = 0.875 terminating decimal 8 1 EXAMPLE#15 Change mixed fraction 3 to a decimal 4 SOLUTION: Ignore the whole number and change the fraction part to decimal number then add it to the whole number part. 0.25 1 1 1 1 Since 3 = 3 + and = 4 100 . , 3 + 0.25 = 3.25 therefore 3 = 3.25 terminating decimal 4 4 4 4 EXAMPLE#13 Change 3 to a decimal 8 0.375 3 3 SOLUTION: 2 + = 2 + 8 3.000 = 2 + 0.375 = 2.375 Therefore 2 = 2.375 8 8 EXAMPLE#16 Change 2